scholarly journals Free Scalar Fields in Finite Volume Are Holographic

Universe ◽  
2019 ◽  
Vol 5 (12) ◽  
pp. 223
Author(s):  
Csaba Balázs
Keyword(s):  
Scalar Field ◽  
Surface Area ◽  
Finite Volume ◽  
Degrees Of Freedom ◽  
Scalar Fields ◽  
Flat Space ◽  
Linear Size ◽  
Energy Mode ◽  
Free Scalar ◽  
Quantized Field

This brief note presents a back-of-the-envelope calculation showing that the number of degrees of freedom of a free scalar field in expanding flat space equals the surface area of the Hubble volume in Planck units. The logic of the calculation is the following. The amount of energy in the Hubble volume scales with its linear size, consequently the volume can only contain a finite number of quantized field modes. Since the momentum of the lowest energy mode scales inversely with the linear size of the volume, the maximal number of such modes in the volume scales with its surface area. It is possible to show that when the number of field modes is saturated the modes are confined to the surface of the volume. Gravity only enters this calculation as a regulator, providing a finite volume that contains the field, the entire calculation is done in flat space. While this toy model is bound to be incomplete, it is potentially interesting because it reproduces the defining aspects of holography, and advocates a regularization of the quantum degrees of freedom based on Friedmann’s equation.

scholarly journals Weak cosmic censorship with self-interacting scalar and bound on charge to mass ratio

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Yan Song ◽  
Tong-Tong Hu ◽  
Yong-Qiang Wang
Keyword(s):  
Scalar Field ◽  
Scalar Fields ◽  
Cosmic Censorship ◽  
Mass Ratio ◽  
Quartic Coupling ◽  
Scalar Theory ◽  
Free Scalar ◽  
The One ◽  
Nonzero Scalar ◽  
Large Charge

Abstract We study the model of four-dimensional Einstein-Maxwell-Λ theory minimally coupled to a massive charged self-interacting scalar field, parameterized by the quartic and hexic couplings, labelled by λ and β, respectively. In the absence of scalar field, there is a class of counterexamples to cosmic censorship. Moreover, we investigate the full nonlinear solution with nonzero scalar field included, and argue that these counterexamples can be removed by assuming charged self-interacting scalar field with sufficiently large charge not lower than a certain bound. In particular, this bound on charge required to preserve cosmic censorship is no longer precisely the weak gravity bound for the free scalar theory. For the quartic coupling, for λ < 0 the bound is below the one for the free scalar fields, whereas for λ > 0 it is above. Meanwhile, for the hexic coupling the bound is always above the one for the free scalar fields, irrespective of the sign of β.

scholarly journals GLOBAL MONOPOLES AND SCALAR FIELDS AS THE ELECTROGRAVITY DUAL OF SCHWARZSCHILD SPACE–TIME

2001 ◽  
Vol 16 (18) ◽  
pp. 1193-1200 ◽  
Author(s):  
NARESH DADHICH ◽  
NARAYAN BANERJEE
Keyword(s):  
Scalar Field ◽  
Equation Of State ◽  
Scalar Fields ◽  
Flat Space ◽  
Space Time ◽  
Global Monopole ◽  
Schwarzschild Solution ◽  
State Formula ◽  
Global Monopoles ◽  
First Time

We prove that both global monopole and minimally coupled static zero mass scalar field are electrogravity dual of the Schwarzschild solution or flat space and they share the same equation of state, [Formula: see text]. This property was however known for the global monopole space–time while it is for the first time being established for the scalar field. In particular, it turns out that the Xanthopoulos–Zannias scalar field solution is dual to flat space.

scholarly journals DYNAMICAL BACKREACTION IN ROBERTSON–WALKER SPACETIME

2011 ◽  
Vol 23 (05) ◽  
pp. 531-551 ◽  
Author(s):  
BENJAMIN ELTZNER ◽  
HANNO GOTTSCHALK
Keyword(s):  
Dynamical System ◽  
Scalar Field ◽  
Stress Tensor ◽  
Einstein Equation ◽  
Scale Parameter ◽  
The State ◽  
Curved Spacetime ◽  
Free Scalar ◽  
Hadamard States ◽  
Quantized Field

The treatment of a quantized field in a curved spacetime requires the study of backreaction of the field on the spacetime via the semiclassical Einstein equation. We consider a free scalar field in spatially flat Robertson–Walker spacetime. We require the state of the field to allow for a renormalized semiclassical stress tensor. We calculate the singularities of the stress tensor restricted to equal times in agreement with the usual renormalization prescription for Hadamard states to perform an explicit renormalization. The dynamical system for the Robertson–Walker scale parameter a(t) coupled to the scalar field is finally derived for the case of conformal and also general coupling.

scholarly journals THE QUANTUM THEORY OF SCALAR FIELDS ON THE DE SITTER EXPANDING UNIVERSE

2008 ◽  
Vol 23 (16n17) ◽  
pp. 2563-2577 ◽  
Author(s):  
ION I. COTĂESCU ◽  
COSMIN CRUCEAN ◽  
ADRIAN POP
Keyword(s):  
Scalar Field ◽  
Gordon Equation ◽  
Scalar Fields ◽  
Wave Functions ◽  
De Sitter ◽  
Scalar Quantum ◽  
Long Time ◽  
Klein Gordon ◽  
Free Scalar ◽  
Special Time

New quantum modes of the free scalar field are derived in a special time-evolution picture that may be introduced in moving charts of de Sitter backgrounds. The wave functions of these new modes are solutions of the Klein–Gordon equation and energy eigenfunctions, defining the energy basis. This completes the scalar quantum mechanics where the momentum basis is well known for long time. In this enlarged framework the quantization of the scalar field can be done in canonical way obtaining the principal conserved one-particle operators and the Green functions.

scholarly journals ON FREE FIELD REALIZATIONS OF STRINGS IN BTZ

2004 ◽  
Vol 19 (10) ◽  
pp. 1579-1588 ◽  
Author(s):  
SAMULI HEMMING
Keyword(s):  
Scalar Field ◽  
Current Algebra ◽  
Free Field ◽  
Scalar Fields ◽  
Spectral Flow ◽  
Free Scalar ◽  
Discrete Representations ◽  
Continuous Representations

We discuss realizations of the SL (2,R) current algebra in the hyperbolic basis using free scalar fields. It has been previously shown by Satoh how such a realization can be used to describe the principal continuous representations of SL (2,R). We extend this work by introducing another realization that corresponds to the principal discrete representations of SL (2,R). We show that in these realizations spectral flow can be interpreted as twisting of a free scalar field. Finally, we discuss how these realizations can be obtained from the BTZ Lagrangian.

QUANTUM CYLINDRICAL WAVES AND PARAMETRIZED FIELD THEORY

2006 ◽  
Vol 15 (10) ◽  
pp. 1743-1752 ◽  
Author(s):  
MADHAVAN VARADARAJAN
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Quantum Gravity ◽  
Flat Space ◽  
Space Time ◽  
Gravitational Fields ◽  
Cylindrical Waves ◽  
Cylindrically Symmetric ◽  
Gravity Effects ◽  
Free Scalar

In this article, we review some illustrative results in the study of two related toy models for quantum gravity, namely cylindrical waves (which are cylindrically symmetric gravitational fields)and parametrized field theory (which is just free scalar field theory on a flat space–time in generally covariant disguise). In the former, we focus on the phenomenon of unexpected large quantum gravity effects in regions of weak classical gravitational fields and on an analysis of causality in a quantum geometry. In the latter, we focus on Dirac quantization, argue that this is related to the unitary implementability of free scalar field evolution along curved foliations of the flat space–time and review the relevant results for unitary implementability.

scholarly journals ON UNITARY TIME EVOLUTION IN GOWDY T3 COSMOLOGIES

2002 ◽  
Vol 11 (09) ◽  
pp. 1451-1468 ◽  
Author(s):  
ALEJANDRO CORICHI ◽  
JERÓNIMO CORTEZ ◽  
HERNANDO QUEVEDO
Keyword(s):  
Scalar Field ◽  
Degrees Of Freedom ◽  
Canonical Quantization ◽  
Quantum States ◽  
Classical Dynamics ◽  
Two Dimensional ◽  
Symplectic Transformation ◽  
Internal Time ◽  
Curved Manifolds ◽  
Free Scalar

A non-perturbative canonical quantization of the Gowdy T3 polarized models is considered here. This approach profits from the equivalence between the symmetry reduced model and 2 + 1 gravity coupled to a massless real scalar field. The system is partially gauge fixed and a choice of internal time is made, for which the true degrees of freedom of the model reduce to a massless free scalar field propagating on a two-dimensional expanding torus. It is shown that the symplectic transformation that determines the classical dynamics cannot be unitarily implemented on the corresponding Hilbert space of quantum states. The implications of this result for both the quantization of fields on curved manifolds and other physically relevant questions regarding the initial singularity are discussed.

scholarly journals ZERO-POINT ENERGY OF MASSLESS SCALAR FIELDS IN THE PRESENCE OF SOFT AND SEMIHARD BOUNDARIES IN D DIMENSIONS

1999 ◽  
Vol 14 (13) ◽  
pp. 2077-2089 ◽  
Author(s):  
F. CARUSO ◽  
R. DE PAOLA ◽  
N. F. SVAITER
Keyword(s):  
Scalar Field ◽  
Energy Density ◽  
Zero Point ◽  
Scalar Fields ◽  
Flat Space ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Zero Point Energy ◽  
Point Energy ◽  
Renormalized Energy

The renormalized energy density of a massless scalar field defined in a D-dimensional flat space–time is computed in the presence of "soft" and "semihard" boundaries, modeled by some smoothly increasing potential functions. The sign of the renormalized energy densities for these different confining situations is investigated. The dependence of this energy on D for the cases of "hard" and "soft/semihard" boundaries are compared.

scholarly journals Black hole hair removal for N = 4 CHL models

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Subhroneel Chakrabarti ◽  
Suresh Govindarajan ◽  
P. Shanmugapriya ◽  
Yogesh K. Srivastava ◽  
Amitabh Virmani
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Degrees Of Freedom ◽  
Microscopic Analysis ◽  
Flat Space ◽  
Special Care ◽  
Hair Removal ◽  
Partition Functions ◽  
Rotating Black Holes

Abstract Although BMPV black holes in flat space and in Taub-NUT space have identical near-horizon geometries, they have different indices from the microscopic analysis. For K3 compactification of type IIB theory, Sen et al. in a series of papers identified that the key to resolving this puzzle is the black hole hair modes: smooth, normalisable, bosonic and fermionic degrees of freedom living outside the horizon. In this paper, we extend their study to N = 4 CHL orbifold models. For these models, the puzzle is more challenging due to the presence of the twisted sectors. We identify hair modes in the untwisted as well as twisted sectors. We show that after removing the contributions of the hair modes from the microscopic partition functions, the 4d and 5d horizon partition functions agree. Special care is taken to present details on the smoothness analysis of hair modes for rotating black holes, thereby filling an essential gap in the literature.

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